I'm firmly in the 'do not finish my words' camp. There isn't one single reason. A lot are mentioned here in the comments already, and honestly I'm really excited to see that. It's a complex thing. Many of us don't want to race you, and we don't want the anxiety that comes along with the feeling of 'competition', and we already struggle with a feeling of insular character as a result of poor expression, so we want to actually own our words. We're putting in the work, we want the payoff. Also, people rarely accurately predict what I'm about to say, which just makes me need to start over again and is a waste of energy for me. But yes, there are also stutterers who don't mind it, and even stutterers who prefer it. I wouldn't usually straight up ask someone not to finish my words unless I knew them well and was sure they'd understand why. This means talking to strangers or new people can be a challenge. So if you want to be extra awesome, then just ask outright what their preference is. And thanks for being so thoughtful!